Average Error: 12.9 → 0.0
Time: 1.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r595251 = x;
        double r595252 = y;
        double r595253 = r595251 * r595252;
        double r595254 = r595252 * r595252;
        double r595255 = r595253 - r595254;
        double r595256 = r595255 + r595254;
        double r595257 = z;
        double r595258 = r595252 * r595257;
        double r595259 = r595256 - r595258;
        return r595259;
}
↓
double f(double x, double y, double z) {
        double r595260 = y;
        double r595261 = x;
        double r595262 = z;
        double r595263 = r595261 - r595262;
        double r595264 = r595260 * r595263;
        return r595264;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot \left(x - z\right)\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))